FFT questions...

Posted by Dean Waldow on Jul 20, 2005; 1:55am
URL: http://imagej.273.s1.nabble.com/FFT-questions-tp3705215.html

Hi Folks,

I have a few FFT related questions. I have tried to look over the  
documentation but have not found answers to my questions as best as I  
can tell or I have missed them.  Any help or suggestion of where to  
find answers would be useful.

Here I refer to PROCESS->FFT->FFT...

1) When taking a FFT of an image that is not 2^Nx2^N, what portion of  
the image is used to do the FFT? For example in a 640x480 image, is  
only a 256x256 subsection used for the FFT?  When I take the FFT of a  
640x480 image, FFT doesn't seem to care that the image is not  
2^Nx2^N.  Or maybe it pads with zeros up to the next 2^Nx2^N?

2) After taking a FFT of an image that is calibrated, you can move  
the cursor over the image and it displays the radius in unit of  
distance / cycle,  angle in degrees, and value of the pixel at that  
r, theta.

     a) How does the radius unit (distance/cycle) relate to a  
scattering wave vector unit (1/distance)?   My thought would be:
             L(distance/cycle = 2*pi / [ wave vector (1/distance) ]

     b) How can I access that radius value from the ip.X which is  
displayed with the cursor is moved over the FFT image? The pixel  
value seems to be accessed in Java via ip.getPixelValue((int)i,(int)
j) (if ip is an imageprocessor variable) but I have not found how the  
radius and theta are accessed for a given pixel. I have I have tried  
a bit to look at the source code but without much luck.

3) What is displayed is said to be the 8 bit power spectrum with log  
scaling after taking an FFT while the 32 bit FHT is attached to the 8  
bit image? Am I close to say that is

         powerspectrum = log ( complex conjugate 32 bit FHT (times)  
32 bit FHT )?

4) Lastly, is there a plugin like radial profile plot (http://
rsb.info.nih.gov/ij/plugins/radial-profile.html) which works with FFT  
images? The radial profile plot plugin appears to ignore the r and  
theta of an FFT powerspectrum image but really seems to have been  
written for real space images.


I have looked at the following documents but likely have missed the  
info:

http://rsb.info.nih.gov/ij/docs/menus/process.html#fft
http://rsb.info.nih.gov/ij/docs/examples/tem/
http://rsb.info.nih.gov/ij/docs/ImageFFT/

Thanks,

Dean
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